A two-stage partial fixing approach for solving the residency block scheduling problem

We consider constructing feasible annual block schedules for residents in a medical training program. We must satisfy coverage requirements to guarantee an acceptable staffing level for different services in the hospital as well as education requirements to ensure residents receive appropriate training to pursue their individual (sub-)specialty interests. The complex requirement structure makes this resident block scheduling problem a complicated combinatorial optimization problem. Solving a conventional integer program formulation for certain practical instances directly using traditional solution techniques will result in unacceptably slow performance. To address this, we propose a partial fixing approach, which completes the schedule construction iteratively through two sequential stages. The first stage focuses on the resident assignments for a small set of predetermined services through solving a much smaller and easier problem relaxation, while the second stage completes the rest of the schedule construction after fixing those assignments specified by the first stage's solution. We develop cut generation mechanisms to prune off the bad decisions made by the first stage if infeasibility arises in the second stage. We additionally propose a network-based model to assist us with an effective service selection for the first stage to work on the corresponding resident assignments to achieve an efficient and robust performance of the proposed two-stage iterative approach. Experiments using real-world inputs from our clinical collaborator show that our approach can speed up the schedule construction at least 5 times for all instances and even over 100 times for some huge-size instances compared to applying traditional techniques directly.